Fractal interfacial enhancement of composite delamination resistance

ABSTRACT

The inventive composite laminate has an interface profile which describes a fractally nonlinear contour. Inventive fabrication thereof typically includes computer numerically controlled wire-cut electrical discharge machining of a metal mold, resin transfer molding of a first composite portion using the metal mold, and resin transfer molding of a second composite portion using the first composite portion as a mold so that the interfacing surfaces of the composite portions are secondarily bonded to each other in conformal fashion. The interface surface of the second composite portion approximates the geometry of the metal mold surface, while the interface surface of the first composite portion approximates the inverted geometry of the metal mold surface. Each interface surface defines a multiplicity of lengthwise parallel grooves and ridges corresponding to the widthwise disordered undulations of the fractal interfacial profile. Both through-thickness strength and fracture toughness can be significantly increased by inventive practice of a composite laminate characterized by fractality of the interfacial profile.

STATEMENT OF GOVERNMENT INTEREST

The invention described herein may be manufactured and used by or forthe Government of the United States of America for governmental purposeswithout the payment of any royalties thereon or therefor.

BACKGROUND OF THE INVENTION

The present invention relates to composite structures and to methods andapparatuses pertaining to same, more particularly wherein the compositestructures are to some degree or in some respect characterized bylamination.

Many composite structures include layers which are bonded together.Various applications have given rise to concern about delaminationresistance at either or both of primary bond sites and secondary bondsites. The term “delamination resistance” is conventionally understoodto encompass “strength” (e.g., through-thickness tensile strength)and/or “toughness” (e.g., Mode I fracture toughness). The terms“through-thickness strength,” “out-of-plane strength” and “interlaminarstrength” are synonymous in conventional usage.

Improvement of the delamination resistance of composite laminates hasbeen attempted through a variety of mechanisms. Among the knownmechanical methodologies for increasing delamination resistance are thefollowing: (i) the insertion of metal pins, stitches or fibrous rodsthrough the thickness of the composite laminate; and, (ii) thealteration of the style of reinforcement, e.g., through utilization oftufted fabrics to improve adhesion. There are drawbacks associated withthese mechanical methodologies, such as cost, degradation of mechanicalproperties in the plane of the laminate, etc. Another conventionalmethodology for enhancing delamination resistance involves toughening ofbrittle resins with particles made of rubber (or another high elongationmaterial); according to these approaches, toughness is generallyachieved at the expense of strength.

It is often desirable to improve both strength and toughness, for theability to do so could delay both crack initiation and crack propagationin composite laminates. Furthermore, any improvements inthrough-thickness strengths in composite laminates can be viewed asadvantageous, since their low strengths in that direction are usuallythe limiting factor in design of structures with composites. Moreover,through-thickness strength is normally very sensitive to quality; thus,improvements in toughness could minimize the flaw sensitivity of thethrough-thickness strength. This is significant particularly becausethrough-thickness stresses tend to arise in structural details which aredifficult to fabricate at the level of quality of flat panels.

Composite structural details for U.S. Navy marine applicationsfrequently require the use of secondary bonds for fabrication in ashipyard environment. Secondary bond sites are interfaces where therehas been lamination over a cured laminate, and they can represent a weaklink in composite laminate performance. The typical microstructuralappearance of a secondary bond is a discrete, linear resin-rich regionbetween the layers of a composite laminate. This resin-rich region canresult in a composite laminate with reduced strengthsthrough-the-thickness of the laminate (i.e., normal to the secondarybond) and reduced resistance to delamination.

SUMMARY OF THE INVENTION

In view of the foregoing, it is an object of the present invention toprovide a composite structure, and method and apparatus for fabricatingsame, wherein the composite structure has superior performance in termsof delamination resistance.

It is a further object of the present invention to provide suchcomposite structure, method and apparatus wherein the delaminationresistance includes either or both of through-thickness strength andfracture toughness.

Another object of this invention is to provide such composite structure,method and apparatus wherein the improvement of delamination resistancewith respect to toughness does not result in the worsening ofdelamination resistance with respect to strength, or vice versa.

A further object of this invention is to provide such compositestructure, method and apparatus wherein the improvement of delaminationresistance does not result in the worsening of a mechanical propertyunrelated to delamination resistance.

Another object of this invention is to provide such composite structure,method and apparatus which are cost-effective.

The present invention features the effectuation of a fractal form ofdisordered geometry at a composite lamina interface. Fractal geometry isadvantageous (vis-a-vis' non-fractally disordered geometry) because itrepresents a reproducible and simplified mathematical regime forintroducing geometric disorder. The disordered interface geometry—andspecific characteristics associated therewith—are inventively related tospecific mechanical or material properties such as through-thicknessstrength and fracture toughness. According to this invention, fractaltopology is not only related to certain material/mechanical properties,but is also used to selectively enhance particular material/mechanicalproperties. In particular, fractal interfaces in composite laminates areinventively used as strengthening and/or toughening mechanisms.

In accordance with this invention, a composite structure comprises afirst lamina and a second lamina. The first lamina has a first laminalsurface which defines a first laminal fractal profile. The second laminahas a second laminal surface which defines a second laminal fractalprofile. The second laminal fractal profile is complementary withrespect to the first laminal fractal profile. The first laminal surfaceand the second laminal surface join so as to form an interface whichdefines an interfacial fractal profile. The interfacial fractal profileis described by the engagement of the first laminal fractal profile andthe second laminal fractal profile.

Also in accordance with this invention, a method for making a compositestructure comprises: providing a metal mold; resin transfer molding afirst lamina; and, resin transfer molding a second lamina. The metalmold has a mold surface which defines a mold fractal profile. The firstlamina has a first laminal surface which defines a first laminal fractalprofile which is effected by the mold fractal profile. The second laminahas a second laminal surface which defines a second laminal fractalprofile which is effected by the first laminal fractal profile.

The present invention admits of embodiments wherein there is secondarybonding of the first lamina and the second lamina, as well asembodiments wherein the first lamina and the second lamina are joined inthe absence of secondary bonding. When secondary bonding is implemented,the inventive composite structure comprises a secondary bond layer whichat least substantially occupies the fractally profiled interface betweenthe first lamina and the second lamina. The inventive fabrication methodcan thus include secondarily bonding the second laminal surface withrespect to the first laminal surface, in association with the resintransfer molding of the second lamina.

The following papers, hereby incorporated herein by reference, discloserelationships between various forms of microstructural disorder andimprovement in various macroscopic properties:

Chen, Z. and Mecholsky, Jr., J. J. September 1993. “Control of Strengthand Toughness of Ceramic/Metal Laminates Using Interface Design.”Journal of Materials Research 8(9):2362-2369;

Tancrez, Jean-Pierre, Pabiot, Jose and Rietsch, Francois. 1996. “Damageand Fracture Mechanisms in Termoplastic-Matrix Composites in Relation toProcessing and Structural Parameters.” Composites Science and Technology56:725-731;

Zumbrunnen, D. A. 1997. “Microstructures and Physical Properties ofComposite Materials Evolved from Chaos.” Proceedings of the FourthExperimental Chaos Conference, Aug. 6-8, 1997, Boca Raton, Fla.

Tancrez et al. disclose improved ductility in toughened polymers wheresmall, non-propagating crases formed a stable “micronet” through which adominant crack would have to propagate.

Zumbrunnen discloses use of chaotic motion to develop very fine-scalemicrostructures and interfaces in two-phase thermoplastic blends.According to Zumbrunnen progressive intertwining of the major and minorphase components led to enhanced material properties (toughness,ductility, strength and electrical conductivity).

Chen et al. disclose in-plane loading of a composite laminate comprisinga brittle alumina layer and a ductile nickel layer. According to Chen etal., the greater the tortuosity (tortuosity quantified by fractals) ofthe interface between alumina and nickel layers in ceramic/metalcomposites, the greater the force required to separate the layers. Chenet al. found that there was an increase in strength, but a decrease intoughness, with increasing fractal dimension (i.e., increasingdisorder). Chen et al. speculate that the decrease in toughness whichthey observed resulted from the inability of the ductile layer toplastically deform as it was constrained by the brittle layer.

As contrasted with Chen et al., Tancrez et al. and Zumbrunnen et al.,the present invention uniquely concerns the relationship of a disorderedinterfacial microstructure of a composite laminate to two specificmacroscopically improved properties, viz., out-of-plane strength andfracture toughness.

It is noted that the analysis and testing performed by the inventors hasinvolved out-of-plane loading, whereas Chen et al. discloses in-planeloading. Chen et al. not only used a different loading direction butalso used different materials. Moreover, Chen et al. addressed aphenomenon which is similar to a known phenomenon which is a manufactureby-product or artifact of linearly interfaced laminates. That is, Chenet al. observed made an observation similar to the observation that theinterface bond geometry of laminates which are essentially linear willbe characterized by disorder along the border or periphery, due toirregularities in fiber packing at such border or periphery.

As distinguished from Chen et al., the present invention uniquelyprovides disorder (in particular, fractality) of the the entire ductile(resin) secondary bond inteface layer, not just of the border orperiphery. The disorder is inventively achieved by using a machined moldplate and by carefully choosing fiber reinforcement so as to ensure thatthe fibers nest in the peaks and valleys of the interface. The inventiveresults of numerical analyses suggest that both strength and toughnessmay be enhanced if small cracks form but do not propagate. In otherwords, the present invention uniquely avails of a newly discoveredrelationship whereby both strength and toughness increase withincreasing disorder; in particular, when the disorder is fractal innature, both strength and toughness increase with increasing fractaldimension.

According to inventive principles, a fractal interface geometry providesbenefits over a more ordered interface geometry through the reduction ofpressure stresses and the introduction of yield stress gradients. Theformation of the small cracks results in the release of constraints toplastic flow. However, the cracks do not propagate, due to thetortuosity of the crack path and to the complex local stress state, bothof which are introduced by the disordered geometry. The small cracksinitiate at sites of localized tensile stress concentration, generallysituated proximate the “maxima” and “minima” of the fractal interfaceprofile. These small cracks act not only as liberators of transverseconstraints to plastic flow, but also as energy-absorbing mechanisms.

The present inventorship includes U.S. Navy employees. Secondary bondsappear frequently in Navy composite structures due to thickness,geometry and fabrication constraints. Secondary bonds represent apotential weak link in the performance of composite structural details,because improper fabrication and assembly may result in lower strengthand toughness at the secondary bond site as compared to the primarystructure. Various embodiments of the present invention can be used toimprove secondary bond strength/toughness or provide alternatefabrication and assembly options. This would result in improvedstructural performance and/or reduced productions costs.

More generally, the inventive utilization of a controlled, disorderedinterface geometry to improve composite strength and toughness in thepresence of through-thickness stresses opens up additional options,beyond material selection, to improve composite structural performanceand efficiency.

Other objects, advantages and features of this invention will becomeapparent from the following detailed description of the invention whenconsidered in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the present invention may be clearly understood, it willnow be described by way of example, with reference to the accompanyingdrawings, wherein like numbers indicate the same or similar components,and wherein:

FIG. 1(a), FIG. 1(b), and FIG. 1(c) are diagrammatic cross-sectionalviews of three interface geometries—viz., linear (square),superimpositionally sinusoidal and fractal, respectively—which were usedas numerical models in inventive finite element analyses.

FIG. 2 is a table of stress summary results obtained from the inventivefinite element analyses of interface models such as shown in FIG. 1(a)through FIG. 1(c).

FIG. 3(a) is a graph illustrating inventive analytical results in termsof peak stress as a function of fractal dimension.

FIG. 3(b) is a graph illustrating inventive analytical results in termsof normalized stress-strain as a function of fractal dimension.

FIG. 4(a) is a diagrammatic perspective view of a metal mold plate uponwhich the first half of the laminate is laid up and cured according toan inventive fabrication embodiment; the metal mold plate is shown tohave a planar mold surface for linear profile and an EDM surface forfractal-like profile.

FIG. 4(b) is a diagrammatic elevation partial view illustratinginventive fabrication using, as a mold, the metal mold plate shown inFIG. 4(a).

FIG. 4(c) is a diagrammatic elevation partial view illustratinginventive fabrication using, as a mold, the lamina shown in FIG. 4(b).

FIG. 4(d) is a diagrammatic elevation view of the inventively fabricatedspecimen which is partially shown in FIG. 4(c), indicating therein afractal-like secondary bond location (region) which was used todetermine through-thickness tensile strength and strain-to-failure inresponse to out-of-plane loading.

FIG. 5 illustrates, in Mathematica format, a formulation of aWeierstrass equation and its corresponding graph, said formulationassociated with the fabrication of a composite laminate having afractal-like interface in accordance with the present invention.

FIG. 6(a) is a black-and-white photograph which provides a magnifiedview (37.5×) of a linear secondary bond region which was the subject ofinventive investigation.

FIG. 6(b) is a black-and-white photograph which provides a magnifiedview (37.5×) of an inventively investigated fractal secondary bondregion such as indicated in FIG. 4(d).

FIG. 6(c) is a black-and-white photograph which provides a magnifiedview (37.5×) of another inventively investigated fractal secondary bondregion such as indicated in FIG. 4(d), this view illustratinginventively undesirable cracking along the secondary bond.

FIG. 7(a) is a diagrammatic partial elevation view of an idealizedinterface profile.

FIG. 7(b) is a partial and enlarged version of the view shown in FIG.7(a), particularly illustrating inventively advantageous cracking alongthe secondary bond.

FIG. 8 is a table of inventive experimental results, including strengthsand strains-to-failure.

BRIEF DESCRIPTION OF THE APPENDICES

The following appendices are hereby made a part of this disclosure:

Attached hereto marked APPENDIX “A” is a copy of a thirty-six pagemanuscript, authored by joint inventors Dale Karr and Karin Gipple,entitled “Fractal Fracture Mechanics of Interlaminar Tensile Failure ofComposites.” This manuscript, hereby incorporated herein by reference,was recently submitted to the International Journal of Fracture, but hasnot as yet been accepted for future publication. Previously, a similarrendering of this manuscript was submitted to, but not accepted forfuture publication by, Mechanics of Materials.

DETAILED DESCRIPTION OF THE INVENTION

One of the present inventors (Karin Gipple, a Navy materials engineer)initially discerned, at a magnification of 10-20×, a qualitativerelationship between through-thickness tension strength of a compositelaminate and its microstructural disorder. Subsequently, she and otherNavy researchers conducted a number of numerical and analytical studiesto investigate and compare the effects of four kinds of secondary bondgeometries (linear, sinusoidal, superimposed sine waves and fractallydisordered) at the interface between layers of a composite laminate. Seethe following paper, hereby incorporated herein by reference: KarinGipple, Dave Plamer, Liming Salvino, Robert Cawley, “Disordercharacterization for Fiber Composite Materials,” FY97 Research Digest,Naval Surface Warfare Center, Carderock Division, issued in April-May1998, pp 47-50.

Referring now to FIG. 1(a) through FIG. 1(c), the Navy researchersexamined stress states in resin-rich layers having geometries whichvaried from linear to superimpositionally sinusoidal to fractal-like. AWeierstrass function was arbitrarily chosen to generate the disordered,fractal-like interface; the fractal interfacial geometry wasapproximated by a truncated Weirstrass series. The resin-rich layerswere embedded within composite laminates subjected to through-thicknessloads.

As shown in each of FIG. 1(a) through FIG. 1(c), the secondary bond site(between first composite layer 17 and second composite layer 21) wascompletely or substantially filled with resin. In FIG. 1(a), linearlyprofiled secondary bond site 31 was formed at the interface betweenfirst linearly profiled composite surface 27 and second linearlyprofiled composite surface 29. In FIG. 1(b), sinusoidally profiledsecondary bond site 61 was formed at the interface between firstsinusoidally profiled composite surface 57 and second linearly profiledcomposite surface 59. In FIG. 1(c), inventive fractally profiledsecondary bond site 25 was formed at the interface between firstfractally profiled composite surface 19 and second fractally profiledcomposite surface 23. Juxtaposed in FIG. 1(c) (proceeding from left toright) are a rectilinear sinusoidal (e.g., square wave) profile, acurvilinear sinusoidal profile, and an inventive fractile-like profile.

With reference to FIG. 2, the numerical evaluations demonstrated that afractal interface geometry reduced the stresses in the bulk of the resinmaterial and concentrated the stresses over small regions in the peaksand valleys of the fractal interface. The results of these analysessuggested to the inventors that more favorable resin stress states areassociated with more disordered interface geometries.

In these tests, a favorable resin stress state was indicated byreduction of normal stresses and introduction of yield stress gradientswithin the resin-rich layer. These results were based on highlyidealized numerical studies. Nevertheless, these results suggested thatthe stress concentration regions may serve as a myriad of crackinitiation sites which are a good energy absorption mechanism, providedthe cracks do not coalesce and propagate.

Based on this experimentation, the inventors speculated that propagationof these cracks would be prevented or delayed by: (i) the fractal paththat the crack would have to follow, and (ii) the unfavorable stressstate (i.e., unfavorable for crack propagation) created by the fractalgeometry. “Unfavorability” in this context entails reduction in thedirect tensile stresses and increase in the shear stresses, therebyallowing for ductile flow, since composite resins are often brittle intension but ductile in shear.

The numerical results suggested that a fractal interface geometry mayprovide benefits over a more ordered interface geometry through thereduction of pressure stresses and the introduction of yield stressgradients. The localized tensile stress concentrations appeared to belikely crack initiation sites, but it was not clear whether cracks wouldpropagate unstably with this geometry and stress state. Analyticalmodels based on crack propagation from a system of pores (See Wimmer, S.A. and Karr, Dale G. 1996. “Compressive Failure of Microcracked PorousBrittle Solids.” Mechanics of Materials 22:265-277, incorporated hereinby reference) were then considered to address microcrack coalescence andpropagation under these conditions.

In a subsequent experimental effort by Navy researchers, the objectivewas to fabricate thick composite laminates with two secondary bondgeometries, linear and fractal-like, at the mid-plane of the laminate.Through-thickness tension specimens cut from these laminates would thenbe used to evaluate through-thickness tension strength andstrain-to-failure (as an indicator of toughness) for the two differentinterface geometries. The laminates would be fabricated using typicalNavy marine production procedures and laminate thicknesses.

Standard Navy composite fabrication procedures result in compositelaminates with a linear secondary bond geometry. Production of acomposite laminate with a disordered secondary bond geometry introducesa number of analytical and fabrication issues. Simplified analyses wererequired to identify key parameters of the disordered profile. These keyparameters then had to be captured in the fabrication of the laminate.

Fractal geometry is a genre of mathematics which is developing as analternative to the more conventional form of geometry, viz., Euclideangeometry. Incorporated herein by reference is the following classictreatise on the subject of fractal geometry, written by one of thepioneers in the field: Benoit B. Mandelbrot, The Fractal Geometry ofNature, New York, N.Y.: W.H. Freeman and Company, 1982. Mandelbrot'swork, which builds particularly on the work of French mathematicianGaston Maurice Julia, has contributed significantly to the developmentof fractal modes of perspective in a variety of scientific and otherdisciplines. See, e.g., Benoit B. Mandelbrot, “A Multifractal Walk downWall Street,” Scientific American, February 1999, pp 70-73, incorporatedherein by reference.

As Mandelbrot discloses in his treatise, Euclidean geometry fails toadequately represent many irregular and fragmented forms in nature.Mandelbrot refers to such shapes as “fractals.” Fractals are manifestedas both two-dimensional and three-dimensional shapes. Fractals arecharacterized by a kind of “self-similarity” and “independence of scale”in the sense that they reveal similar shapes on both smaller and largerscales. As understood by those who are ordinarily skilled in the art, afractal can be generated to the desired level of precision byimplementing an iterative or recursive function.

A well known type of fractal dimension is known as the“Hausdorff-Besicovich” dimension. According to Mandelbrot, a fractal isdefined by its topological dimension and by its Hausdorff-Besicovichdimension. The topological dimension is the conventional sense ofdimension; e.g., the topological dimension of a point is 0, thetopological dimension of a line is 1, the topological dimension of asurface is 2, the topological dimension of a solid such as a sphere orcube is 3, etc. Hence, the topological dimension is always an integer;however, the Hausdorff-Besicovich dimension is not necessarily aninteger. The Hausdorff-Besicovich dimension is always greater than orequal to the topological dimension. Roughly speaking, the fractaldimension of an object is calculated by taking the limit, as the scaleof measurement approaches zero, of the following quotient: log (changein size of object)/log (change in scale of measurement).

Referring to FIG. 3(a) and FIG. 3(b), and also referring to APPENDIX A,which is incorporated herein by reference, parametric studies of afractal interfacial geometry were performed, based on fractal fracturemechanics, in accordance with principles, methods and techniquesdescribed in the aforementioned manuscript by Karr and Gipple, containedin APPENDIX A, entitled “Fractal Fracture Mechanics of InterlaminarTensile Failure of Composites.”

Let us designate the fractal dimension “D,” and designate “D*” thefractal dimension differential, i.e., the difference between the fractaldimension D and the topological dimension. Since the present inventionis primarily concerned with a profile manifested as a single line whichlies in a single plane and is characterized by some degree oftortuosity, the topological dimension of interest herein is one. We thusestablish a relationship between D and D* wherein D=D*+1, or D*=D−1. Thederivation of Equation 1, set forth hereinbelow, is contained inAPPENDIX A. The non-dimensional peak stress is designated “{tilde over(σ)}*.” Non-dimensional peak stress {tilde over (σ)}* expressed as afunction of fractal dimension D, where D*=D−1, is given by Equation 1and is illustrated in FIG. 3(a).

 {tilde over (σ)}*=[ξ^(D*)(1+D*)(1−D*)^((1−D*))(D*)^(D*)]^(½)

In Equation 1, ξ=(I₀/η*), where I₀ is half of the initial crack lengthand η* is a lower bound on the resolution scale. For D*=0, D=1; hence,the analysis reduces to that of linear elastic fracture mechanics.

It is expected that ξ, a nondimensional scaled crack length parameter,will be much greater than 1, since an accurate estimate of length wouldrequire resolution at a finer scale than that of the profile beingmeasured. Crack growth would proceed in a stable manner at stressesbelow the peak stress. From previous finite element analyses, hightriaxial normal stresses in the resin region between composite layerswere localized in the peaks and valleys of the fractal interfacialgeometry. It is likely that cracks would initiate in those locations sothat I₀ might be a function of the width of the peaks and valleys of thefractal profile.

The preceding analysis is based on a single, isolated fractal crack. Adamage mechanics approach was used to examine the relationship betweencrack density and stiffness for multiple fractal cracks, andlocalization theory was used to predict material failure. See APPENDIXA. FIG. 3(a) shows curves of the peak stress as functions of D* forvarious values of ξ. FIG. 3(b) shows potential changes in thestrain-to-failure for different values of D* assuming a crack density of0.1 and ξ equal to 10.

As shown in FIG. 3(a), there is an increase in the peak stresses as thefractal dimension is increased. In fact, the normalized peak stress σ*is shown to be highly dependent on both ξ and D*. The fracture strengthcan evidently be increased substantially by increasing the fractaldimension of the crack profile and by establishing a fine scalesubstructure. These effects increase the surface energy asssociated withfractal crack growth.

It is noted that Chen et al., discussed previously herein, wereconcerned with fractal dimensions on the order of 1.2. It is seen inFIG. 3(a) that, as a general rule, the peak stress does notsignificantly increase until the fractal dimension D reaches a value ofapproximately 1.4. Also, as a general rule, the peak stress does notsignificantly increase until the fineness of scale ξ reaches a value ofapproximately 10. Therefore, a useful “rule of thumb” for inventivepractice provides at least one of: (i) a fractal dimension of at least1.4; and, (ii) a fineness of scale of at least 10. That is, inventivepractice preferably effectuates either a fractal dimension of at least1.4, or a fineness of scale of at least 10, or both a fractal dimensionof at least 1.4 and a fineness of scale of at least 10. Moreover, auseful general observation of the interplay between fractal dimension Dand scale fineness ξ is that, as scale fineness ξ increases, a givenincrease in fractal dimension D will more steeply increase peak stress.

As shown in FIG. 3(b), there is a considerable increase in thestrain-to-failure. For a single fractal crack, the peak stress isachieved which is associated with the material's strength. Thesestrengths, however, may not be reached because of the occurrence oflocalization. The localization stress levels for each particular caseare somewhat less than the peak stress, but this reduction is rathersmall; therefore, peak stresses are often a good approximation ofmaterial strength. The strains-to-failure, on the other hand, may beconsiderably less when localization conditions are considered. Thus, theadditional strain energy absorbed during loading can be limited tovalues considerably below those predicted by analysis of single fractalcracks.

The term “tortuosity” refers to the degree of path complexity of thefractal crack profile. The tortuosity of the fractal profile can beexpressed, for example, as [(mean path length)/(minimum possible pathlength)]²; however, it may be more meaningful, for inventive purposes,to consider the tortuosity to be characterized by the fractal dimensionD. That is, the tortuosity varies in accordance with the fractaldimension D.

In sum, the fractal fracture mechanics according to this inventionindicate the preferability of high values for fractal dimension D aswell as high values for fineness of scale ξ. “High values for fractaldimension D” is equivalently stated as “high values for fractaldimension differential D*” or as “high tortuosities.” As shown in FIG.3(a), fractal dimension differential D* and fineness of scale ξ,considered together, are predictive of normalized peak stress {tildeover (σ)}* As shown in FIG. 3(b), for a given fineness of scale ξ,increase in fractal dimension differential D* results in increase inpeak stress {tilde over (σ)}*. FIG. 3(a) and FIG. 3(b) together revealthat the higher the value of such given scale fineness ξ, the moreabrupt is the increase in peak stress {tilde over (σ)}* in accordancewith increase in fractal dimension differential D*. In addition, as morefully discussed hereinbelow, the widths of the “peaks” and “valleys” ofthe machined fractal interface should be on the order of at least oneand preferably several fiber diameters.

The experimental aspect of this program was an attempt to captureelements of the analysis in the fabrication of a composite laminate witha fractal-like secondary bond geometry. Every effort was made tosimulate the standard Navy composite marine fabrication procedures.

The inventively required features of the interface introduced a numberof fabrication issues that are not typically encountered in compositesecondary bonding procedures. The desirable features of the secondarybond region based on analysis results included: a profile that was fineenough in scale relative to the fiber diameter; nesting of the fibers inthe peaks/valleys of the profile; a disordered distribution of thepeaks/valleys in the profile; and, a geometry that introduced multiaxialstresses within the resin rich layer.

To elaborate, there was a need for a fine scale to the disorder (on theorder of the fiber diameter or a few multiples thereof). The amplitudeof the disorder needed to be on the order of a layer or lamina thicknessso that the ductile resin layer could be transversely constrained by thestiffer surrounding composite (resin plus fiber) layers. There was aneed for angled shear planes to allow shear flow of the resins; marinecomposite resins/adhesives are often brittle in tension but ductile inshear. There was a need for a disordered distribution of cracks ratherthan an ordered distribution of cracks.

Reference now being made to FIG. 4(a) through FIG. 4(d), fabrication ofa composite laminate having a secondary bond usually requires a moldplate upon which the first half of the laminate is assembled. Aftercure, the first half of the laminate is used as the mold plate for thesecond half. Normally, the mold plate has a linearly profiled (e.g.,smooth and planar) surface. In accordance with the present invention, aportion of the mold plate has a fractally profiled (e.g., irregular anddisordered) surface.

An inventive steel mold plate 11 (such as shown in FIG. 4(a)), havingfractally profiled mold plate surface 13 and linearly profiled moldplate surface 15, was fabricated with approximate dimensions 2 incheswide×10 inches long×0.25 inches thick. Fractally profiled surface 13 wasproduced via wire EDM (Electrical Discharge Machining) using 0.004 inchdiameter wire. Fractally profiled mold plate surface 13 has a pluralityof mold plate surface peaks 12 and of mold plate surface valleys 14. Inperspective, fractally profiled surface 13 appears as an irregularconfiguration of alternating peaks 12 and valleys 14, wherein peaks 12are parallel longitudinal ridges which are erratically shaped and sized,and valleys 14 are parallel longitudinal grooves which are erraticallyshaped and sized.

EDM is a conventional material-removal technique which uses electricityunder carefully controlled conditions to remove metal by means of sparkerosion. The three basic components of the EDM process are an electrode(a cutting tool), a dielectric fluid and a conductive workpiece.Generally, a series of rapidly recurring electrical discharges isapplied, in the presence of a dielectric field, between the electrodeand the workpiece. The resultant tiny metal chips are removed by meltingand vaporization, and are washed away by the dielectric fluid (which iscontrolled so as to provide continuous rinsing).

According to EDM, the electrode never touches the workpiece; rather, acontrolled spark from the electrode to the workpiece (this small sparkoccurring thousands of times per second) causes a small portion of theworkpiece to melt and vaporize—that is, causes the workpiece to be cutor formed. The dielectric fluid (typically, a nonconductive liquid suchas deionized water or oil) helps to create and control the spar,provides a shield between the electrode and the workpiece, serves as acoolant to to keep the workpiece cool, and serves as a flushing agent toremove resolidified particles from the cutting area. The workpiece canbe any conductive material, including many types of metals.

EDM can create many forms and shapes into the workpiece, depending uponthe configuration and motion of the electrode. “Wire EDM” (alternativelyreferred to as “wirecut EDM” or “wire-cut EDM”) implements a travellingwire electrode. The continuously spooling conducting wire electrodemoves in preset patterns around the workpiece. Tool wear is avoided inthis manner, for the wire is constantly being replenished. Normally, thewire is controlled using CNC (Computer Numerical Control). Navyresearchers effectuated wire EDM using CDC for purposes of making theworkpiece, viz., inventive steel mold plate 11.

In the light of this disclosure, the ordinarily skilled artisan will becapable of performing EDM using CNC, for purposes of practicinginventive fabrication. Some pertinent U.S. patents, hereby incorporatedherein by reference, are the following: Sato et al. U.S. Pat. No.5,756,956 issued May 26, 1998; Seki et al. U.S. Pat. No. 5,025,363issued Jun. 18, 1991; Ito et al. U.S. Pat. No. 4,839,487 issued Jun. 13,1989; Ito et al. U.S. Pat. No. 4,806,721 issued Feb. 21, 1989; ObaraU.S. Pat. No. 4,649,252 issued Mar. 10, 1987; Shichida et al. U.S. Pat.No. 4,123,645 issued Oct. 31, 1978.

As shown in FIG. 4(b), composite part 17, approximately 0.5 in thick,was then fabricated implementing mold plate 11, using a VARTM processonto mold plate 11. The first half of the laminate was laid up and curedupon fractally profiled mold plate surface 13, yielding first compositepart 17 having first fractally profiled composite surface 19. The resinwas a vinylester 510A. The fiber was an E-glass woven roving orunidirectional fabric.

As shown in FIG. 4(c), first composite part 17 was then implemented asthe mold for second composite part 21. Second composite part 21 wasfabricated using a VARTM process onto first composite part 17. Thesecond half of the laminate was laid up and cured upon first fractallyprofiled composite surface 19, yielding second composite part 21 havingsecond fractally profiled composite surface 23. The combined thicknessof mated composite parts 17 and 21 was approximately 1 inch.

As shown in FIG. 4(c), secondary bond site 25 was established at theinterface between composite part 17 and composite part 21. Morespecifically, fractally profiled secondary bond site 25 was formed atthe interface between first fractally profiled composite surface 19 andsecond fractally profiled composite surface 23. Linearly profiledsecondary bond site 31 (like in FIG. 1(a)) was formed at the interfacebetween first linearly profiled composite surface 27 and second linearlyprofiled composite surface 29.

Fractally profiled secondary bond site 25 revealed a fractal-likeprofile commensurate with the meshing of fractally profiled compositesurface 19 with second fractally profiled composite surface 23.Geometrically speaking, and with some approximation, fractally profiledmold plate surface 13 could be thought of as an inverted-image twin tofirst fractally profiled composite surface 19, and as an identical twinto second fractally profiled composite surface 23. In other words, thefractal profile of mold plate surface 13 is approximately congruent withthe fractal profile of composite surface 23, and is invertedlyapproximately congruent with the fractal profile of composite surface19.

First fractally profiled composite surface 19 has first compositesurface peaks 18 and first composite surface valleys 20 which areanalogues of mold plate surface valley 14 and mold plate surface peak12, respectively. Second fractally profiled composite surface 23 hassecond composite surface peaks 22 and second composite surface valleys24 which are analogues of mold plate surface peak 12 and mold platesurface valley 14, respectively.

Bearing in mind that the peaks and valleys describe a fractal profile,and hence attempts to attribute regularity thereto have limited meaning,it may nonetheless be useful to consider that, very roughly speaking,there is alternation of peaks 18 and valleys 20, and alternation ofpeaks 22 and valleys 24. When first fractally profiled composite surface19 and second fractally profiled composite surface 23 are closely unitedand secondarily bonded so as to form fractally profiled secondary bondsite 25, peaks 18 fit within valleys 24 with approximate coincidence,and peaks 22 fit within valleys 20 with approximate coincidence.

Once mated, composite parts 17 and 21 each represented a layercomprising a fiber-reinforced matrix material—i.e., a resin togetherwith continuous, longitudinally unidirectional fiber reinforcement. Thefibers were disposed in the direction of the “grooves” and “ridges”defined by peaks 18 and 22 and valleys 20 and 24. Composite parts 17 and21 were joined at their respective fractally profiled surfaces 19 and 23so that some of the fibers of composite part 17 were nested withinvalleys 24, and some of the fibers of composite part were nested withinvalleys 20.

Fractally profiled secondary bond site 25 and linearly profiledsecondary bond site 31 each represented an intermediate layer comprisinga ductile resin. Typically, this type of three-layer compositearrangement (i.e., a sandwich of two composite layers and a secondarilybonding resin therebetween) constitutes a portion of an entire compositelaminate, wherein there are many alternations of a fiber-reinforcedresin layer and a secondary bond resin layer running through thethickness of the composite laminate.

To elaborate on the above-described inventive fabrication process, thesurface of steel mold plate 11 was used to control the geometric profileof the secondary bond. As shown in FIG. 4(a), inventive mold plate 11had a fractally profiled mold plate surface 13, as well as alinearly-profiled mold plate surface 15. The surface of steel mold plate11 was machined using a computer numerically controlled (CNC) electricaldischarge machining (EDM) procedure. This computer algorithmic controlof EDM is illustrated in FIG. 5.

With reference to FIG. 5, the numerical profile was defined using thefollowing recursive function, a truncated Weierstrass model (5 terms),to obtain the fractal-like surface: 0.00632 [sin(2πx)−(1/⁵2)sin(4πx)+(1/⁵2)² sin(8πx)−(1/⁵2)³ sin(16πx)+(1/⁵2)⁴ sin(32πx)−(1/⁵2)⁵sin(64πx)]. This mathematical definition was chosen solely for thepurposes of specificity and repeatability. In the light of thisdisclosure, it is understood by the ordinarily skilled artisan thatinventive practice of EDM using CNC can include effectuation of any of amultitude of recursive functions for purposes of generating the fractalinterface.

The fineness of the scale of the profile was limited by the wirediameter used in the wire-cut EDM procedure. The profile was cut with a0.004″ wire, which was the smallest feasible wire size. However,breakage of the thin wire limits the feed rates, which in turn limitsthe width of the mold plate.

The small size of mold plate 11 limited the number of specimens thatcould be obtained from each fabrication iteration. The risk of materialquality variations within the laminate was also greater as there waslittle excess material to trim from the edges of the laminate which aretypically of poorer quality.

As stated earlier herein, the nesting of reinforcing fibers within thefractal-like profile was a desirable feature. Samples were fabricatedwith two types of fabrics and a vinylester resin (room temperature cure)using a SCRIMP® process—that is, in accordance with methods andtechniques disclosed in William H. Seemann, III U.S. Pat. No. 4,902,215issued Feb. 20, 1990, entitled “Plastic Transfer Molding Techniques forthe Production of Fiber Reinforced Plastic Structures,” said U.S. Pat.No. 4,902,215 hereby being incorporated herein by reference. The SCRIMPtechnology, disclosed in said U.S. Pat. No. 4,902,215, is proprietary toTPI Composite, Inc., Melville Facility, 225 Alexander Road, Portsmouth,R.I. 02871. The word “SCRIMP,” a registered trademark of TPI Composite,Inc., is acronymous for “Seemann Composites Resin Infusion MoldingProcess.”

Typical Navy applications use a 24 oz., E-glass woven roving fabric. Thecoarseness of this fabric and its bi-directionality (warp and weft tows)made it likely that it would not nest or fully drape into the machinedprofile of the mold plate. As expected, the 24 oz fabric did not followthe profile, but sat on top resulting in a thick linear resin layer atthe secondary bond interface. Dow Corning donated a number ofunidirectional glass fabrics held together with propylene stringers. Theunidirectional fabric resulted in damaged specimens with cracks alongthe stringers.

Composite part 17 was fabricated with 24 oz. woven roving strandshand-placed along the “grooves” (mold plate surface valleys 14) in mold11. The surface of mold 11 had a baked-on mold release agent which waschosen to minimize contamination of surface 19 and secondary bond site25.

According to typical SCRIMP procedures, after the first piece is removedfrom the mold, the surface of the first piece is sanded so as to removeany residual mold release agent. Sanding in this case, however, woulddestroy the desired fractal-like surface 19 profile of composite part 17(the first half of the laminate). Following removal from mold plate 11,first fractally profiled composite surface 19 was wiped with acetone.Woven roving strands were laid up by hand on this composite part 17surface. Infusion of vinylester resin completed the secondary bonding ofcomposite part 21 (the second half of the laminate) to composite part17.

The final composite product, shown in FIG. 4(c), was approximately 8″ by4″. Four to five specimens 33 with a fractal-like secondary bond andfour specimens 35 with a linear secondary bond could be obtained fromthat piece. Such a fractal secondary bond specimen 33 or linearsecondary bond specimen 35 can be considered to be diagrammaticallyrepresented in FIG. 4(d), wherein the secondary bond site can beconceived to define, as the case may be, either a fractally profiledsecondary bond 25 or a linearly profiled secondary bond 31. The linearsecondary bond specimens 35 were obtained from laminate that extendedbeyond fractally profiled surface 13, onto linearly profiled surface 15,of the machined metal mold 11. Through-thickness loading L_(T-T) wasapplied to each specimen as shown in FIG. 4(d).

Referring to FIG. 6(a) through FIG. 6(c), photomicrographs were taken ofthe secondary bond region for both the linear and fractal-likegeometries. Overall, as shown in FIG. 6(b), nesting of the fibers alongthe interface is good. Ideally, though, the fractal-like profiles wouldhave much sharper peaks and valleys relative to the fiber diameter.

Another fabrication quality-related issue with the fractal-like bond isshown in FIG. 6(c), which is a photomicrograph of a portion of afractal-like bond showing voids and pre-existing cracks existing in thevicinity of the interface. These unwanted inherent (pre-loading) defectsare distinguishible from the beneficial small cracks which are shown inFIG. 7(b).

Referring to FIG. 7(a) and FIG. 7(b), ideally, secondary bond profile 25should be “sharper” (i.e., have a greater scale fineness ξ) than thatwhich is shown in FIG. 4(c). The present invention seeks to establish asecondary bond profile which succeeds in achieving a desirable mode ofsmall crack propagation akin to that shown in FIG. 7(b). However, theattainable fineness of scale ξ may be limited by practicalconsiderations. In inventive practice, the fineness of scale ξ may beupwardly limited by the fact that the diameter of the wire used in theEDM processing of metal mold 11 is downwardly limited; that is, 0.004inches, and possibly 0.002 inches, appears to be the smallest feasiblewire size. Theoretically speaking, the smaller the EDM wire diameter,the better; practically speaking, an EDM wire diameter between about0.002 inches and 0.004 inches is practicable.

As shown in FIG. 7(b), first composite part 17 and second composite part21 have first fibers 41 and second fibers 43, respectively. Peaks 18each comprise some first fibers 41 which nest in a valley 24. Similarly,peaks 22 each comprise some second fibers 43 which nest in a valley 20.The small cracks 50 are inventively propagated, at sites which are at ornear the maxima of peaks and the minima of valleys, as a consequence ofthrough-thickness loading such as that which the specimen is subjectedto as shown in FIG. 4(d).

Reference is now made to FIG. 8, wherein strengths andstrains-to-failure are tabularly represented. Only two specimens wereavailable from the linear secondary bond section. One to two specimensfrom each group (linear and fractal-like) failed prematurely, possiblydue to bending from load train misalignment, which is a commondifficulty with this test method. Failure in each case was catastrophic.

Strengths from the specimens with a fractal-like secondary bond wereapproximately 20% greater and strain-to-failure was 75% greater thancomparable results for specimens with a linear bond geometry. Each typeof specimen exhibited linear stress-strain behavior, but the modulus ofthe fractal-like bond specimens was significantly lower than that of thelinear bond specimens. The presence of cracks in the specimen prior totesting may be the cause of the reduced modulus.

However, the elevated strength of the fractal-like bond relative to thelinear bond (more typical of current standard practices) is encouraging.The photomicrograph of the fractal-like bond and these strengthincreases generally correlates with the analyses illustrated in FIG.3(a). That is, these limited data suggest that ξ was low (machinedprofile correlates to D* of 0.8) or that the in-situ profile achievedwas of a lower fractal dimension.

The strength and strain-to-failure increases are promising indicationsthat disordered bond line geometries can improve through-thicknessstrengths, but further fabrication and testing efforts are required tovalidate these trends. To more fully evaluate the influence of the bondline disorder on the through-thickness strength, several steps should betaken. Additional specimens should be fabricated following the sameprocedures but attempting to eliminate cracks and voids near theinterface.

The possibility of mold release contamination of the secondary bondregion in the fractal-like case should be considered. Alternate and moredisordered profiles in the secondary bond region could be fabricated andtested looking for increases in strength, nonlinear stress-strainbehavior and increased strain-to-failure as compared to this set ofdata. Testing of future specimens should include four gages around thecircumference of the gage section to detect the presence of bending.

Other embodiments of this invention will be apparent to those skilled inthe art from a consideration of this specification or practice of theinvention disclosed herein. Various omissions, modifications and changesto the principles described may be made by one skilled in the artwithout departing from the true scope and spirit of the invention whichis indicated by the following claims.

What is claimed is:
 1. A composite structure comprising a first laminaand a second lamina, said first lamina having a first laminal surfacewhich defines a first laminal fractal profile, said second lamina havinga second laminal surface which defines a second laminal fractal profilewhich is complementary with respect to said first laminal fractalprofile, said first laminal surface and said second laminal surfacebeing complementarily joined so as to form an interfacial region whichdefines an interfacial fractal profile which is described by theengagement of said first laminal fractal profile and said second laminalfractal profile, said interfacial region being bounded by said firstlaminal surface and said second laminal surface, said interfacialfractal profile being bounded by said first laminal fractal profile andsaid second laminal fractal profile, said interfacial region being atleast substantially characterized by longitudinal constancy of saidinterfacial fractal profile through said interface in an orthogonaldirection with respect to an imaginary vertical plane which passesthrough said first laminal fractal profile, said second laminal fractalprofile and said interfacial fractal profile, wherein: said firstlaminal surface describes an arrangement of first longitudinalelevations and first longitudinal depressions; said second laminalsurface describes an arrangement of second longitudinal elevations andsecond longitudinal depressions; said first longitudinal elevations matewith said second longitudinal depressions; said second longitudinalelevations mate with said first longitudinal depressions; saidlongitudinal constancy is manifested by said first longitudinalelevations, said first longitudinal depressions, said secondlongitudinal elevations and said second longitudinal depressions; saidfirst lamina includes a first resin and a plurality of firstunidirectional fibers which are disposed in said first resin in anorthogonal direction with respect to said imaginary vertical plane; saidsecond lamina includes a second resin and a plurality of secondunidirectional fibers which are disposed in said second resin in anorthogonal direction with respect to said imaginary vertical plane; somesaid first unidirectional fibers are disposed in said first longitudinalelevations; and some said second unidirectional fibers are disposed insaid second longitudinal elevations.
 2. A structure as in claim 1,wherein: said first longitudinal elevations are each characterized by afirst elevational profile width; said second longitudinal elevations areeach characterized by a second elevational profile width; said firstlongitudinal depressions are each characterized by a first depressionalprofile width; said second longitudinal depressions are eachcharacterized by a second depressional profile width; said firstlongitudinal unidirectional fibers are each characterized by a firstfibrous width; said second longitudinal unidirectional fibers are eachcharacterized by a second fibrous width; each of said first elevationalprofile width and said second depressional profile width is at least asgreat as three said first fibrous widths; and each of said secondelevational profile width and said first depressional profile width isat least as great as three said second fibrous widths.
 3. A structure asin claim 2, wherein said first laminal fractal profile, said secondlaminal fractal profile and said interfacial fractal profile are eachcharacterized by a fractal dimension of at least approximately 1.4 and ascale fineness of at least approximately
 10. 4. A structure as in claim1, wherein said composite structure comprises secondary bond materialwhich at least substantially occupies said interfacial region.
 5. Astructure as in claim 1, wherein said first lamina is at leastsustantially composed of a first polymer matrix composite material,wherein said second lamina is at least sustantially composed of a secondpolymer matrix composite material, and wherein said structure has beenmade by the method comprising: providing a metal mold having a moldsurface which defines a mold fractal profile, said providing includingrendering said mold fractal profile in accordance with a recursivemathematical function; resin transfer molding said first lamina, saidresin transfer molding said first lamina including using said metalmold, said first laminal surface thereby being effected by said moldsurface so that said first laminal fractal profile is complementary withrespect to said mold fractal profile; and resin transfer molding saidsecond lamina, said resin transfer molding said second lamina includingusing said first lamina, said second laminal surface thereby beingeffected by said first laminal surface so that said second laminalfractal profile is complementary with respect to said first laminalfractal profile.
 6. A structure as in claim 1, wherein: said firstlongitudinal elevations are each characterized by a first elevationalprofile depth; said second longitudinal elevations are eachcharacterized by a second elevational profile depth; said firstlongitudinal depressions are each characterized by a first depressionalprofile depth; said second longitudinal depressions are eachcharacterized by a second depressional profile depth; said firstlongitudinal unidirectional fibers are each characterized by a firstfibrous width; said second longitudinal unidirectional fibers are eachcharacterized by a second fibrous width; each of said first elevationalprofile depth and said second depressional profile depth is at least asgreat as three said first fibrous widths; and each of said secondelevational profile depth and said first depressional profile depth isat least as great as three said second fibrous widths.
 7. A structure asin claim 1, wherein: said first lamina includes a first resin and aplurality of first unidirectional fibers which are disposed in saidfirst resin in an orthogonal direction with respect to said imaginaryvertical plane; said second lamina includes a second resin and aplurality of second unidirectional fibers which are disposed in saidsecond resin in an orthogonal direction with respect to said imaginaryvertical plane; some said first unidirectional fibers are disposed insaid first longitudinal elevations; and some said second unidirectionalfibers are disposed in said second longitudinal elevations.
 8. Astructure as in claim 7, wherein said composite structure comprisessecondary bond material which at least substantially occupies saidinterfacial region.
 9. A structure as in claim 5, wherein: said firstlamina includes a first resin and a plurality of first unidirectionalfibers which are disposed in said first resin in an orthogonal directionwith respect to said imaginary vertical plane; said second laminaincludes a second resin and a plurality of second unidirectional fiberswhich are disposed in said second resin in an orthogonal direction withrespect to said imaginary vertical plane; some said first unidirectionalfibers are disposed in said first longitudinal elevations; and some saidsecond unidirectional fibers are disposed in said second longitudinalelevations.
 10. A structure as in claim 9, wherein said compositestructure comprises secondary bond material which at least substantiallyoccupies said interfacial region.
 11. A structure as in claim 5, whereinsaid composite structure comprises secondary bond material which atleast substantially occupies said interfacial region.
 12. A structure asin claim 6, wherein said composite structure comprises secondary bondmaterial which at least substantially occupies said interfacial region.13. A composite structure comprising a first lamina and a second lamina,said first lamina having a first laminal surface which defines a firstlaminal fractal profile, said second lamina having a second laminalsurface which defines a second laminal fractal profile which iscomplementary with respect to said first laminal fractal profile, saidfirst laminal surface and said second laminal surface beingcomplementarily joined so as to form an interfacial region which definesan interfacial fractal profile which is described by the engagement ofsaid first laminal fractal profile and said second laminal fractalprofile, said interfacial region being bounded by said first laminalsurface and said second laminal surface, said interfacial fractalprofile being bounded by said first laminal fractal profile and saidsecond laminal fractal profile, said interfacial region being at leastsubstantially characterized by longitudinal constancy of saidinterfacial fractal profile through said interface in an orthogonaldirection with respect to an imaginary vertical plane which passesthrough said first laminal fractal profile, said second laminal fractalprofile and said interfacial fractal profile, wherein: said compositestructure comprises secondary bond material which at least substantiallyoccupies said interfacial region; said first laminal surface describesan arrangement of first longitudinal elevations and first longitudinaldepressions; said second laminal surface describes an arrangement ofsecond longitudinal elevations and second longitudinal depressions; saidfirst longitudinal elevations mate with said second longitudinaldepressions; said second longitudinal elevations mate with said firstlongitudinal depressions; said longitudinal constancy is manifested bysaid first longitudinal elevations, said first longitudinal depressions,said second longitudinal elevations and said second longitudinaldepressions; said first lamina includes a first resin and a plurality offirst unidirectional fibers which are disposed in said first resin in anorthogonal direction with respect to said imaginary vertical plane; saidsecond lamina includes a second resin and a plurality of secondunidirectional fibers which are disposed in said second resin in anorthogonal direction with respect to said imaginary vertical plane; somesaid first unidirectional fibers are disposed in said first longitudinalelevations; and some said second unidirectional fibers are disposed insaid second longitudinal elevations.
 14. A structure as in claim 13,wherein: said first longitudinal elevations are each characterized by afirst elevational profile width; said second longitudinal elevations areeach characterized by a second elevational profile width; said firstlongitudinal depressions are each characterized by a first depressionalprofile width; said second longitudinal depressions are eachcharacterized by a second depressional profile width; said firstlongitudinal unidirectional fibers are each characterized by a firstfibrous width; said second longitudinal unidirectional fibers are eachcharacterized by a second fibrous width; each of said first elevationalprofile width and said second depressional profile width is at least asgreat as three said first fibrous widths; and each of said secondelevational profile width and said first depressional profile width isat least as great as three said second fibrous widths.
 15. A structureas in claim 14, wherein said first laminal fractal profile, said secondlaminal fractal profile and said interfacial fractal profile are eachcharacterized by at least one of: a fractal dimension of at least about1.4; and a scale fineness of at least about
 10. 16. A structure as inclaim 13, wherein said first lamina is at least sustantially composed ofa first polymer matrix composite material, wherein said second lamina isat least sustantially composed of a second polymer matrix compositematerial, and wherein said structure has been made by the methodcomprising: providing a metal mold having a mold surface which defines amold fractal profile, said providing including rendering said moldfractal profile in accordance with a recursive mathematical function;resin transfer molding said first lamina, said resin transfer moldingsaid first lamina including using said metal mold, said first laminalsurface thereby being effected by said mold surface so that said firstlaminal fractal profile is complementary with respect to said moldfractal profile; and resin transfer molding said second lamina, saidresin transfer molding said second lamina including using said firstlamina, said second laminal surface thereby being effected by said firstlaminal surface so that said second laminal fractal profile iscomplementary with respect to said first laminal fractal profile.
 17. Amatrix composite laminate comprising first and second layers which joinso as to form a tortuous interface, wherein: said first layer includesplural parallel linear first fibers; said second layer includes pluralparallel linear second fibers; said first and second fibers are parallelto each other; said first layer has a tortuous first face; said secondlayer has a tortuous second face; said tortuous first face has pluralfirst ridges and plural first grooves which are parallel to each otherand to said first and second fibers; said tortuous second face hasplural second ridges and plural second grooves which are parallel toeach other and to said first and second fibers; said first ridges, saidfirst grooves, said second ridges and said second grooves are parallelto each other; some said first fibers are placed in said first ridges;some said second fibers are placed in said second ridges; said firstface is characterized by a first face fractality which manifests in thedirection perpendicular to said first and second ridges and first andsecond grooves; said second face is characterized by a second facefractality which manifests in the direction perpendicular to said firstand second ridges and first and second grooves; said tortuous interfaceis characterized by an interface fractality which manifests in thedirection perpendicular to said first and second ridges and first andsecond grooves; said first face fractality and said second facefractality are inversely congruent, said first face fractality and saidsecond face fractality thereby meshing with each other, said first facefractality and said second face fractality thereby defining saidinterface fractality, said first ridges thereby fitting said secondgrooves, said second ridges thereby fitting said first grooves, saidfirst and second ridges and first and second grooves thereby definingsaid tortuous interface; said first face is characterized by at leastapproximate linearity which manifests in the direction of said first andsecond ridges and first and second grooves; said second face ischaracterized by at least approximate linearity which manifests in thedirection of said first and second ridges and first and second grooves;said tortuous interface is characterized by at least approximatelinearity which manifests in the direction of said first and secondridges and first and second grooves; said first face fractalitymanifests approximately identically at at least substantially alllocations along said first and second ridges and first and secondgrooves; said second face fractality manifests approximately identicallyat at least substantially all locations along said first and secondridges and first and second grooves; and said interface fractalitymanifests approximately identically at at least substantially alllocations along said first and second ridges and first and secondgrooves.
 18. A matrix composite laminate as recited in claim 17, whereinsaid first face fractality, said second face fractality and saidinterface fractality are each indicative of the same recursivemathematical function.
 19. A matrix composite laminate as recited inclaim 17, wherein: each said first ridge has nested therein a pluralityof said first fibers; each said second ridge has nested therein aplurality of said second fibers; said tortuous interface generallydescribes an imaginary interface plane; said plurality of said firstfibers includes at least three said first fibers which lie in a firstimaginary plane which is parallel to said first imaginary plane; andsaid plurality of said second fibers includes at least three said secondfibers which lie in a second imaginary plane which is parallel to saidimaginary interface plane.
 20. A matrix composite laminate as recited inclaim 19, wherein said first face fractality, said second facefractality and said interface fractality each have a fractal dimensionof at least approximately 1.4.